HUGH ROSE The Johns Hopkins University A Policy Rule for ‘Say’& law’ in a Theory of Temporary Equilibrium* In a theory of temporary macroeconomic equilibrium this paper considers whether there is a simple nondiscretionary rule of monetary management under which the free play of market forces will always equate aggregate money demand to the sum of expected money incomes, whatever the latter may be, so that aggregate demand ceases to be a determinant of the economy’s behavior. The rule proposed is that the Central Bank should let the commercial banks determine their cash reserves by trading negotiable securities with it at current prices. The conditions for the rule’s success are given and are supported by theoretical considerations. 1. Introduction The purpose of this paper is to ask in what circumstances a simple, nondiscretionary policy rule proposed for the Central Bank will cause the free play of market forces to generate an aggregate of money demand and money income exactly equal to the sum of expected money incomes, whatever the latter may be, so that ag- gregate demand ceases to be a determinant of the economy’s be- havior. One might say that the question is whether “Say’s Law of Markets” can be imposed whenever we wish. For if the rule is effective, the market mechanism itself guarantees that supply, as measured by the sum of expected money incomes, creates its own demand. Monetary macroeconomics has proceeded for many years un- der the supposition that Say’s Law cannot prevail and that one must live with the “problem of aggregate demand.” If this is not the case after all, the consequences are obviously far-reaching. So long as the policy were sustained, the economy would be completely in- sulated from shocks arising on the side of aggregate demand, and from revisions of income expectations induced by unexpected total money incomes, with their expansionary or contractionary conse- quences. The general business cycle would be due only to shocks *I am deeply indebted to Carl Christ, Edi Karni, Masahiro Kawai, Peter New- man, and especially to Louis Maccini, for helpful discussion and comments. Journal of Macroeconomics, Winter 1985, Vol. 7, No. 1, pp. 1-17 1 Copyright 0 1985 by Wayne State University Press.
Transcript
HUGH ROSE The Johns Hopkins University
A Policy Rule for ‘Say’& law’ in a Theory of Temporary Equilibrium*
In a theory of temporary macroeconomic equilibrium this paper considers whether there is a simple nondiscretionary rule of monetary management under which the free play of market forces will always equate aggregate money demand to the sum of expected money incomes, whatever the latter may be, so that aggregate demand ceases to be a determinant of the economy’s behavior. The rule proposed is that the Central Bank should let the commercial banks determine their cash reserves by trading negotiable securities with it at current prices. The conditions for the rule’s success are given and are supported by theoretical considerations.
1. Introduction The purpose of this paper is to ask in what circumstances a
simple, nondiscretionary policy rule proposed for the Central Bank will cause the free play of market forces to generate an aggregate of money demand and money income exactly equal to the sum of expected money incomes, whatever the latter may be, so that ag- gregate demand ceases to be a determinant of the economy’s be- havior. One might say that the question is whether “Say’s Law of Markets” can be imposed whenever we wish. For if the rule is effective, the market mechanism itself guarantees that supply, as measured by the sum of expected money incomes, creates its own demand.
Monetary macroeconomics has proceeded for many years un- der the supposition that Say’s Law cannot prevail and that one must live with the “problem of aggregate demand.” If this is not the case after all, the consequences are obviously far-reaching. So long as the policy were sustained, the economy would be completely in- sulated from shocks arising on the side of aggregate demand, and from revisions of income expectations induced by unexpected total money incomes, with their expansionary or contractionary conse- quences. The general business cycle would be due only to shocks
*I am deeply indebted to Carl Christ, Edi Karni, Masahiro Kawai, Peter New- man, and especially to Louis Maccini, for helpful discussion and comments.
Journal of Macroeconomics, Winter 1985, Vol. 7, No. 1, pp. 1-17 1 Copyright 0 1985 by Wayne State University Press.
Hugh Rose
impinging on the conditions of supply: no unexpected money in- come would arise to cause or aggravate it, nor indeed to mitigate it. Unemployment would not be brought about by deficiency of the aggregate demand for output. The rate of inflation of money income would be determined by and equal to built-in expectations of it: the policy would therefore be neither a direct cause of inflation nor an instrument for altering it. Thus one would not introduce it at a time of excessive inflation.
There is admittedly a risk that an economy being run in neu- tral gear, as it were, could be liable to volatility of inflationary ex- pectations, because any change in them would be self-justifying. But since the magnitude of this risk cannot be objectively estimated a priori, it cannot constitute a fundamental objection until the pol- icy has been practiced and found wanting in this respect. What one does know a priori is that such changes would not be the result of excessive aggregate demand.
The rule I propose is intended to let the nominal stock of money be generated by the demand for it. The Central Bank, in- stead of controlling member banks’ cash reserves by active trading in securities at their current prices, should stand passively ready to deal in them with the banks, still at their current prices, in ex- change for reserves. So long as the Central Bank does so, the mem- ber banks can alter their reserves to any desired extent by trading securities with it.
The inquiry then can be divided into two parts: (a) If this rule does cause the total stock of nominal money
to be demand-generated, will Say’s Law be imposed by it?
(b) Will the rule cause the total money stock to be de- mand-generated?
The basic theory required is of a temporary macroeconomic equilibrium, and is developed in Section 2. Section 3 is concerned with (a). Since (a) can be discussed, without much loss of generality, in abstraction from the commercial banking system, the model of these two sections uses the simplifying assumption that all money is the liability of a Central Bank; the proposed rule then becomes an undertaking by the Central Bank to trade negotiable securities passively with anyone, at their current prices, in exchange for de- posits or notes. In Section 2 the money stock is fixed by the Central Bank. In Section 3 the Central Bank follows this rule, which suc-
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ceeds in making the stock of money demand-generated. The con- sequence depends crucially on whether there is some passive net hoarding of unexpected incomes. Say’s Law will follow if and only if there is such a hoarding. This condition is essentially that the “loanable funds” theory of interest, not the “liquidity preference” theory, should be valid, and there is a strong argument in favor of the former.
Section 4 enlarges the model to include the commercial banks, with a view to discussing (b). The answer to (b) depends on whether commercial banks can create derivative deposits or not. If they can, the proposed rule must fail. If they cannot, the rule will impose Say’s Law, provided, of course, that there is some passive net hoarding of unexpected incomes. I suggest a justification of the view that the banks cannot.
My thesis is that we can impose what I have called Say’s Law by means of the proposed rule. The conclusions are summarized more precisely in Section 5.
For the theory of temporary equilibrium, and for some of the notation and terminology, I have drawn on Keynes’s Treatise on Money [(1930), Chapters g-111, but with two modifications. The first, which Keynes himself introduced in the General Theory [(1936), Chapter 51, is that current employment depends on short-term, not long-term, expectations. The second is a generalization which allows both theories of interest to be considered. (I hope to deal with these and related matters in the history of thought on another occasion.)
2. Temporary Equilibrium without Commercial Banks To tackle the problem as I have formulated it, one needs a
model of a momentary or temporary equilibrium. In the closed economy, to which my analysis is restricted, there must be a tem- porary equilibrium both of the market for final output and of the market for securities or loanable funds; otherwise there is no scope for the play of market forces. As to existence of the equilibrium, I shall simply assume it. Conditions for its local stability are given, but proof of their sufficiency is omitted for lack of space.
One also needs to make the temporary equilibrium of any in- stant (arbitrarily short interval) depend parametrically on the sum of money incomes expected to accrue in it, and therefore on the expectations of current prices and real factor incomes entertained at its outset. To justify this, I shall assume that entrepreneurs wish to choose their labor force at the outset of the interval, before
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knowing what actual prices, or demands, will emerge in it. This is because nonhomogeneity of labor creates costs of hiring and firing people at short notice. Firms pick the number of people to employ at the outset by maximizing expected current profits on their cur- rent capital. Thus in relation to the events of any instant, both labor (in the sense of the number of people employed) and capital are fixed factors. The temporary equilibrium (TE) is like the shortest- run Marshallian market equilibrium, relative to which all factors are fixed for the individual entrepreneur. Within the interval, however, high or low actual prices, or demands, may induce more or less intensive use of the factors, the latter including temporary shut- downs and layoffs, so that a difference of realized from expected TE money incomes may arise from high or low production from the factors on hand as well as from high or low prices.
I shall use the term “windfalls” for the sum of unexpected money incomes, which may be positive (windfall gains) or negative (windfall losses). If they persist, windfall gains lead to more favor- able (windfall losses to less favorable) expectations in subsequent intervals, so that as time passes expected money incomes will rise (or fall) faster than they would otherwise; and unless money wages are perfectly flexible, so also will expected real income and em- ployment rise or fall. The Say’s-Law policy would (if effective) pre- vent all this by ensuring that whatever expectations are held at the outset of an interval windfalls in it turn out to be zero.
Let Y be the flow of total real income currently expected in consequence of firms’ maximization of expected profits, and let p be the level of expected prices associated with Y, such that pY is the sum of money incomes expected for the current instant. Both p and Y are parameters with respect to the events determining the current TE. The flow of actual money income is pY + Q’, where Q’ is windfalls. But since it is convenient to work with variables deflated by p, I define Q by the identity pQ = Q’. The flow of actual money income is then p(Y + Q).
Let Z(Q, r; Y, K) and C(Q, r; Y, K) be the flows of planned investment and consumption demand (money values deflated by p). Here r is “the” interest rate on nonmoney claims (an index of the whole complex of such rates), and K is the stock of capital. Since Y and K enter as parameters for any TE, we may suppress them, abbreviating to Z(Q, r) and C(Q, r). While the ensuing analysis would be unaffected if neither Z nor C depended on Q, it is in- cluded for the sake of generality. The sign of Co is ambiguous, because a positive income effect may be outweighed by an inter-
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‘Say’s Law’ in Theory of Temporary Equilibrium
temporal substitution effect of actual prices in relation to p. I, should be nonpositive, because planned inventory investment is apt to vary inversely with the ratio of actual prices to p, and temporary income seems an unlikely stimulant of other investment.
In the closed economy actual money income is the value of final output. With government spending included in Z and C, the excess demand for final output, deflated by p, is
Xg = Z(Q, r) + C(Q, r) - Y - Q . (1)
Planned saving (deflated by p) is defined as S = Y - C, so that S = S(Q, r; Y, K), or, in the abbreviated form, S(Q, r). Then
X, = Z(Q> r) - S(Q, 4 - Q . (2)
Actual prices, or production from the factors on hand, or both, respond positively to X,. It is assumed, therefore, that
DO = Q& > (3)
where D = d/dt and Ed is a positive adjustment coefficient. Let L(Q, r; Y, K) be the stock demand for money (here Cen-
tral-Bank money), nominal demand deflated by p. Abbreviating, as with the other functions, we write it L(Q, r). Here, too, Q is in- cluded for the sake of generality. In the present model, from which commercial banks are excluded, we might expect L, to be non- negative. In the wider setting, however, it may be negative. For windfalls may inversely affect the demand for bank loans (for ex- ample, if they reduce desired inventories), and, since borrowers may want to keep some portion of their loans on deposit, as a safety- margin above their anticipated outlays, or may be required to do so by the banks, the demand for deposits may be inversely related to Q.
The nominal stock of money is M’, and M’ = pM defines M as nominal stock deflated by p. Changes in M in the adjustment to TE are changes in M’.
The flow demand for money is the sum of the active net hoarding and passive net hoarding of money balances. The former occurs because the stock of money differs from the demand for it, and is assumed to be y(L - M), where y is a positive adjustment coefficient. The latter occurs to the extent that windfall gains are temporarily added to money balances, rather than being instantly
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lent as they accrue, and windfall losses are temporarily subtracted from money balances, rather than being instantly financed. It is as- sumed to be CYQ (0 I o 5 l), with cx constant. The (p-deflated) flow excess demand for money is then
X, = y[L(Q, r) - M] + aQ - DM . (4)
From the fact that the net increase of the money stock plus money income equals the sum of the plans for investment, con- sumption, net hoarding of money balances, and net lending in the widest sense, we obtain the identity (Walras’ Law)
x, = x, + x,n > (5)
where X, is the (p-deflated) excess demand for loanable funds. Sub- stituting from (2) and (4), we have
We then have r responding positively to Xf, and it is assumed that
Dr = qXf, (7)
4 being a positive adjustment coefficient. The passage to a TE is assumed to occur in an instant, in
“auctioneer’s time, ” as it were. In this section the Central Bank chooses M’ at the outset of the instant, so that M is a parameter and DM = 0. A TE is an equilibrium solution of (3) and (7), or equivalently a zero of the functions X, in (2) and Xr in (6), given M and that DM = 0. The equations for it are
‘The question examined in this paper does not depend on how Q* is split into its price-quantity components, i.e., on the nature of the TE supply function. If X is the volume index of final output and n its price level, money income p(Y + Q) = nX, so that n = pY/X + pQ/X. -In the TE n* = pY/X + p(Z - S)/X. This is equivalent to Keynes’s Fundamental Equation (iv), Treatise, Chapter 10, p. 137. To determine n* we need, in addition to the equations for market clearing, an as- sumption about X as a function of Y and Q. Keynes apparently assumed it pro- portional to Y, for his windfalls are entirely entrepreneurial profits or losses.
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‘Say’s Law’ in Theory of Temporary Equilibrium
It is therefore characterized by (8) and
a[Z(Q*, r*) - S(Q*, r*)] = $M - L(Q*, r*)] . (10)
For uniqueness of the TE, and for its local asymptotic stability regardless of the relative magnitudes of the adjustment coefficients, l g, l f and y, it is sufficient that the following inequalities should be satisfied:
I, - s, < 0, I, - s, - 1 = I, + c, - 1 < 0, L, < 0 A = (IQ - S, - l)L, - (Zr - S,)L, > 0 . (11)
The condition A > 0 is obviously redundant unless L, is negative. From (10) it is apparent that the TE conditions depend on
whether there is some passive net hoarding or not. If not, i.e., if (Y is zero, (10) reduces to
L(Q*> r*) = M . (12)
The TE rate of interest equates the stock demand for money to the stock supply.” Equations (8) and (9) show why this is so. Z - S is matched in the funds market [Equation (9) with 01 = 0] by financial transactions of equal magnitude, namely Q*, because there are im- mediate net loans of windfalls equal to it.
But if (Y is positive, Z - S is not fully matched financially by net loans from windfalls, because there is some passive net hoard- ing of them. Active net dishoarding must fill the gap, The TE rate of interest must stand above or below the level that equates L and M, according to whether Z - S is positive or negative.3
deed, Active net dishoarding is equal to passive net hoarding. In-
Y(M - L) = ctQ* (13)
follows immediately from X, = 0. We can also interpret (13) as saying that active net dishoarding is sustained by passive net hoard- ing: “yesterday’s” passive net hoarding becomes “today’s” active net
*This is Keynes’s “liquidity-preference” theory. 3The “loanable funds” theorists assumed cx = 1. But the essential point in their
theory is that a is positive.
Hugh Rose
dishoarding, for passive hoarding is a temporary expedient, not a permanent increase in the demand for money.
It is shown in Section 3 that the condition cx > 0 is critical for the success of the policy rule aimed at Say’s Law. But rational conduct would seem to demand it. For a = 0 means that unex- pected receipts are not allowed to increase money balances, nor unexpected payments to reduce them, even momentarily, i.e., dur- ing any period of operational time, however short. The theory of the precautionary demand for money implies that this cannot be an optimum strategy. Nonmoney claims lack liquidity partly, at least, because the terms for unexpected purchases and sales of them at short notice are apt to be disadvantageous in comparison with the terms for expected transactions in them. There should therefore be a temporarily passive response to unexpected net receipts, i.e., pas- sive net hoarding of them.
It may be helpful to close this section by exemplifying a longer- run adjustment of the economy in this TE. For instance, consider how the familiar Keynesian model of a short-period underemploy- ment equilibrium, given K, can emerge from the TE theory as a special case of the economy’s response to nonzero Q*. For this pur- pose our TE may be expressed by the equations
Z(Q*, r*, Y) - S(Q*, r*, Y) = Q* ;
dZ(Q*> r*, Y) - S(Q*, r*, VI = yW/p - UQ*, r*> VI ;
together with
Y = F(N), pF’(N) = w,
where N is the number of people employed, w is the money wage, M’ is nominal money, and perfect competition is assumed. The last equation is necessary for the maximization of expected profits on a given capital.
If, when Q* is nonzero, money-income expectations for suc- cessive instants are revised rapidly in comparison with changes of w and M’ (and, of course, K), i.e., if sign DpY = sign Q*, given w and M’ as parameters, the TE converges to the short-period equilibrium, whose equations are
I@, r*, Y*) = S(0, ?-*, y*) )
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‘Say’s Law’ in Theory of Temporary EquiZibrium
p*L(O, r*, Y*) = M’ ,
Y* = F(N*) ,
p*F ‘(N*) = w ,
provided that, in addition to the inequalities in (ll), the well-known condition (I, - S,)L, - (I, - S,)Ly > 0 is satisfied. The adjustment of the sum of expected money incomes until it is equal to actual money income has determined the short-period level of employ- ment.
3. The Say%-Law Policy in the Absence of Commercial Banks I assume that, for any given p and Y, there is a stock of nom-
inal money that implies Q * = 0 and r* > 0. The TE equations with it are
Z(0, r*) = S(0, r*) L(0, r*) = M* ’ (14)
This zero-Q TE is unique, because of I, - S, < 0. It is the situation in which aggregate money demand is equated to the given sum of expected incomes.
In this section, as in the last, all money is the liability of a single Central Bank. The policy rule I am proposing, in order to obtain this TE through the otherwise unassisted play of market forces, is, in this simplified context, an undertaking by the Central Bank to trade negotiable securities passively with anyone, at their current prices, in exchange for deposits or notes. When the public has more or less money than it wishes to hold, the public can change that money by trading securities with the Central Bank, and has an in- centive to do so. For in (6) above, the closer DM is to active net hoarding, y(L - M), the less interest rates are moved against the active net hoarders: if the two were equal, active net hoarding would have no tendency to move interest rates at all, because the terms would offset each other in X,. It can therefore be assumed that some positive fraction, 8, of active net hoarding will seek the outlet offered by the Central Bank, i.e.,
DM = &y[L(Q, r) - M] , (0 < 0 I 1) . (15)
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(It is not necessary to assume that all active net hoarding takes this form, i.e., that 8 = 1.)
The assumption that DM depends only on active net hoarding, not also on passive net hoarding of windfalls (crQ), is not an arbi- trary one. The latter is an accumulation of money received from the sale of goods. It therefore cannot be the direct cause of an inflow of new money.
There are now three differential equations, for Q, r, and M, namely (3), (7), and (15). For X, we still have
X, = Z(Q> 4 - S(Q, r) - 0. (2)
On substituting (15) into (6) we obtain
Xf = Z(Q> 4 - S(Q, d - Q + (1 - ‘3y[L(Q, r) - Ml + aQ . (16)
A TE is an equilibrium solution of the differential equations, and a zero of the functions X, in (2), X, in (16), and L(Q, r) - M.
If a is positive, it is easily verified that the unique solution is (14). The inequalities of (11) guarantee its local asymptotic sta- bility, regardless of the relative magnitudes of eg, l f and y. Say’s Law prevails. That part of the finance for I - S which must come from active net dishoarding is withdrawn, as active net dishoarding is itself eliminated by the public’s disposition to change M, with the result that the market cannot support a nonzero Z - S.
But if (Y is zero, the situation is quite different. The conditions X, = X, = L - M = 0 imply only that
Z(Q*, r*) - S(Q*, r*) = Q* L(Q*> r*) = M” (17)
In fact there is a multiplicity of equilibria. (14) is among them; but, since in its neighborhood there is a continuous locus of others, in all of which Q* is nonzero, (14) cannot be an asymptotically stable equilibrium of the differential equations. The Banks rule does not succeed. The effect of active net hoarding on M is simply to render indeterminate the equilibrium at which I - S is matched financially by net loans from windfalls.
We have established the proposition that when the Central Bank permits DM to be determined by the public’s active net hoarding Say’s Law prevails if and only if there is some passive net hoarding of windfalls.
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‘Say’s Law’ in Theory of Temporary Equilibrium
4. The Model with Commercial Banks There are two theories of the dynamic genesis of bank de-
posits. The earlier, based on the “law of reflux,” was totally ousted by the theory of “derivative deposits” [Phillips (1920) and Crick (1951)], until the case for it was reopened by Tobin (1963). In this section they are examined for their implications in the TE model and, briefly, for their credentials.
Derivative Deposits The logical basis for this theory is the conception of commer-
cial banks as price-taking portfolio-selectors [for a treatment, see Porter (1961)]. G iven the banks’ current deposits, expected yields, and expected loan rates, they choose the optimum proportion of each asset, including bank loans, to their deposits, while the market determines actual yields and loan rates in an auction. There is a net creation of deposits whenever there is active net dishoarding of banks’ cash reserves, unless a contemporaneous net reduction of total reserves offsets it. Without this offset active net dishoarding by the banks constitutes a net increase of their earning assets, and so also of their deposits. The public is temporarily constrained to accept the net increment of deposits as part of its passive net hoard- ing, for it has no opportunity to change any of the quantities of the banks’ earning assets.
For the TE model I shall simplify by abstracting from the note issue. Let A4 now be total deposits, and let R be the banks’ total cash reserves at the Central Bank, both nominal quantities deflated by p. L(Q, r) is the public’s stock demand for deposits. The banks’ stock demand for reserves is CM, with c a constant. (The subse- quent analysis is not affected by this further simplification.)
The flow excess demand for money, including both deposits and reserves, is
X, = y(L - M) + P(cM - R) + (cxQ + DM) - DM - DR. (18)
The first two terms are active net hoarding of deposits and reserves respectively, y and B being positive adjustment coefficients. The term oQ + DM is passive net hoarding, including the public’s pas- sive net hoarding of the net increment of deposits. Since +DM and - DM cancel.
X, = y(L - M) + P(cM - R) + (YQ - DR , (19)
and, from (2), (5), and (19), the flow excess demand for funds is
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Hugh Rose
Xf= Z(Q> 4 - S(Q> 4 - Q + y[UQ, r) - Ml
+ @(CM - R) + ciQ - DR. (20)
Consider first the case where the Central Bank chooses R at the outset of any instant, so that R is parametric and DR = 0. The net creation of (derivative) deposits then equals the banks’ planned net dishoarding:
DM = P(R - CM) . (21)
There are three differential equations, in Q, r, and M, namely (3), (7), and (21). A TE is a zero of the functions X, in (2), X, in (20) with DR = 0, and R - CM. The inequalities of (11) are sufficient for its uniqueness and local asymptotic stability. Its equations are
The banks have their desired ratio of reserves to deposits. If o. is zero, the stock of deposits equals the demand for them, but if (Y is positive, there is in general active net hoarding by the public. In neither case, however, has the stock of deposits been generated by the demand for them.
Now if, instead of fixing R as above, the Central Bank adopted our policy rule, undertaking to trade securities with the banks, at their current prices, in exchange for reserves, the result would not be Say’s Law. Indeed, one can see without formal analysis that the result would probably be disastrous, and, if not disastrous, then certainly futile.
It would be disastrous if, as seems likely, some banks justi- fiably expect to lose to others only a part of the deposits created by their own dishoarding. Under the assumed policy they could safely sell securities to the Central Bank for extra reserves and buy securities in the market and extend loans in excess of the extra reserves. R and M would expand indefinitely, so long as such banks could find profitable investments for extra deposits. There would be runaway inflation of money income.
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It would be futile if every bank fears that the whole change of deposits caused by its own net dishoarding may occur in other banks, so that the only motive the banks have for altering their reserves is to move them towards CM. In a TE the ratio R*/M* would be c, but the magnitude of M* would depend fortuitously on how much of the gap between CM and R had been eliminated via changes in derivative deposits and how much via changes in reserves. There would be a multiplicity of possible equilibria, each looking like (22) and each corresponding to some indeterminate out- come for R* and M*. There would be no tendency whatever to- wards the zero-Q TE.
The “Law of Reflux” The derivative-deposit theory depends in an essential way on
the hypothesis that banks are price takers and quantity makers in regard not only to their portfolio of negotiable securities but also to their loans. For if, in regard to their loans, they are price makers and quantity takers, their net dishoarding of reserves (unaccompa- nied by a net reduction of reserves) does not constitute a net in- crease of their earning assets and deposits because the public is not constrained to accept any incipient change of deposits as passive net hoarding; on the contrary, the public can prevent any undesired change of deposits by altering its borrowing from the banks. Fur- thermore, the public can determine, if necessary through the same channel, what the net increment of deposits shall be in accordance with its own active net hoarding, and has an incentive to do so in that the tendency of interest rates to move against the net hoarders of deposits is diminished to the extent that their active net hoarding brings about a net increase of deposits. This is in essence the “law of efflux and reflux” applied to modern banking.
That banks are indeed price makers in regard to their loans is supported not only by common observation but also by the na- ture of their loans as contractual agreements, embodying the banks’ services as specialists in the market for funds. By monitoring bor- rowers’ activities they are able to provide better terms than would be obtainable from nonspecialists, who are not in as good a position to protect themselves against default risk. At optimally chosen loan rates (in competition with other market rates, of course) they should want to accommodate all creditworthy borrowers, since their spe- cialist activity is their main source of profits. Thus in regard to their loans they are both price makers and quantity takers vis-a-vis the market as a whole. It follows from this, and from the fact that loans
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can be repaid at any time, that the public determines the volume of bank loans at rates of interest set by the banks.
To incorporate this theory of deposit genesis in the extended TE model, two changes are necessary. First, in the flow excess de- mand for money, including both deposits and reserves, DM should not occur in the term for passive net hoarding, since it cannot be forced on an unwilling public. Instead of (18), therefore, we have
X, = y(L - M) + @(CM - R) + aQ - DM - DR. (23)
Secondly, DM is determined, not by the derivative-deposit equa- tion (21), but by the “net efflux” equation
DM = e$L(Q, 4 - Ml > (24)
with 6 assumed constant and 0 < 8 5 1. Some part of the public’s active net hoarding of deposits causes the net increase of deposits, if necessary through the channel afforded by its control over the volume of bank loans.
From (2), (5), (23), and (24) the flow excess demand for funds becomes
X, = Z(Q, r) - S(Q, 4 - Q + (1 - eML(Q, r) - Ml
+ P(cM - R) + aQ - DR. (25)
As before, consider first the case where R is parametric. The three differential equations, in Q, r, and M, are (3), (7), and (24), and the TE is a zero of the functions X, in (2), X, in (25) with DR = 0, and L(Q, r) - M. It is given by the equations:
Given (ll), the TE is unique. However, (11) is not quite enough to guarantee local stability independently of the adjustment coef% cients. It does imply that all real roots are negative, but to rule out the posibility of explosive oscillations we require also that
L, I 0. (27)
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‘Say’s Law’ in Theory of Temporary Equilibrium
(If eg were small enough in relation to er, the possibility would not materialize, even if L, were positive.)
In the TE the public has the deposits it wants to hold. If cx is zero, the banks’ stock demand for reserves is likewise satisfied; the TE is indistinguishable from that of the derivative-deposit the- ory. But if (Y positive, there is active net dishoarding by the banks, not, as in the previous theory, by the public, to finance a(Z - S).
The equation of active net dishoarding to passive net hoarding now takes the form
P(R - c&f*) = OLQ*. (28)
This can be given the following interpretation: Windfalls that ac- crued “yesterday” to the banks as passively hoarded reserves are actively dishoarded by them “today,” and windfalls that accrued “yesterday” to the public as passively hoarded deposits are used by the public “today” to cancel the deposit-increment that would oth- erwise result from the banks’ active dishoarding “today.” In effect “today’s” a(Z - S) is financed by “yesterday’s” passive hoarding, which is put back into circulation by the banks’ active dishoarding.
Turning now to the question of Say’s Law, assume that the Central Bank stands passively ready to trade negotiable securities with the banks, at their current prices, in exchange for reserves. Since the banks cannot create derivative deposits, their only motive for changing their reserves is to bring them into equality with CM. Both convenience and economic incentive should induce them to accomplish some part of their net hoarding via the Bank, the in- centive being the tendency of security prices to move against them when they go to the market instead of the Bank [see (25)]. Con- sequently there will be a “net efflux” equation for reserves,
DR = /J$(cM - R) ) (29)
where i.~ is the proportion of the banks’ active net hoarding that takes advantage of the Central Banks undertaking. lo is assumed to be constant, and 0 c IA I 1.
The result is that Say’s Law will be imposed if and only if (Y is positive. On substituting (29) into (25) we obtain
X, = Z(Q> r) - S(Q, 4 - Q + (1 - e)$L(Q, 4 - Ml
+ (1 - /JJB(cM - Z-I) + CXQ . (30)
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Hugh Rose
There are four differential equations, in Q, r, M, and R, namely (3), (7), (24), and (29). The TE is a zero of the functions X, in (2), Xf in (30), L(Q, r) - M, and CM - R.
If (Y is positive, the unique solution is the extended version of (14):
L(0, r*) = M* . (31)
R*=cM*
The banks’ disposition to change R eliminates their active net dis- hoarding, withdrawing the support for nonzero I - S.
Both (11) and (27) are in general required to guarantee local stability independently of the adjustment coefficients. [If p, = 1, (27) is not needed. If both p. and 0 are unity, the stability condi- tions reduce to Zo - So - 1 < 0 and I, - S, < 0.1
But if (Y is zero, there is the same indeterminacy, for the same reason, as in the simple model of Section 3.
The proposition that has been established is that Say’s Law will be imposed by the policy rule suggested for the Central Bank, if and only if (a) there is some passive net hoarding of windfalls, and (b) bank deposits are generated by the public’s active net hoarding of them, not by the banks’ active net dishoarding of re- serves.
5. Conclusions A model of temporary macroeconomic equilibrium has been
constructed and used to examine the question whether there is a simple policy rule for the Central Bank under which the free play of market forces, unassisted by discretionary government interven- tions, can be invoked to ensure that, whatever the sum of expected money incomes may be, there will be generated an aggregate of money demand and realized money incomes exactly equal to it, so that aggregate demand ceases to be a determinant of the economy’s behavior. The rule proposed is an undertaking by the Central Bank to stand passively ready to trade negotiable securities, at their cur- rent prices, with the commercial banks in exchange for cash re- serves. The rule will achieve its object if and only if (a) there is some passive net hoarding of unexpected incomes, and (b) bank de-
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‘Say’s Law’ in Theory of Temporary Equilibrium
posits are generated by the public’s active net hoarding of them, not by the banks’ active net dishoarding of reserves. Arguments have been offered in favor of both these conditions.
Received: August 1983 Final version received: October 1984
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Keynes, J.M. A Treatise on Money. London: Macmillan, 1930. -. The General Theory of Employment, Interest and Money.
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